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This is a real pain and I'm getting nowhere. If you can't see the image look at the attached file.

Angle a(upper angle)=Theta Angle b(lower angle)=Beta

Prove these relations:

a) Rsin2theta+d(1+cos2theta)=(R^2)/Rnot where Rnot= ((vnot)^2)/g

b) That Rm(meaning maximum R) happens for tan2(thetamax)=Rm/d

c) 2thetamax+alpha=90 degrees

d) (Rnot^2)+2dRnot=Rm^2

For a) I'm getting down to 2costheta(Rsintheta+dcostheta)=(R^2)/Rnot

But I don't see the next step, maybe I went too far. Or do I need to include Beta somewhere? I don't think I do. There is some trig relation or relating it to the diagram that I just don't see.

All I really need is help on a)then

I can use what I know from a) to solve for b) and each one after can be done likewise however I won't get to them if I can't get a) done.

Please HELP!

Angle a(upper angle)=Theta Angle b(lower angle)=Beta

Prove these relations:

a) Rsin2theta+d(1+cos2theta)=(R^2)/Rnot where Rnot= ((vnot)^2)/g

b) That Rm(meaning maximum R) happens for tan2(thetamax)=Rm/d

c) 2thetamax+alpha=90 degrees

d) (Rnot^2)+2dRnot=Rm^2

For a) I'm getting down to 2costheta(Rsintheta+dcostheta)=(R^2)/Rnot

But I don't see the next step, maybe I went too far. Or do I need to include Beta somewhere? I don't think I do. There is some trig relation or relating it to the diagram that I just don't see.

All I really need is help on a)then

I can use what I know from a) to solve for b) and each one after can be done likewise however I won't get to them if I can't get a) done.

Please HELP!